What is expand (x^3-6x^2+12x-8)/(x-2) ?

The solution to expand (x^3-6x^2+12x-8)/(x-2) is x^2-4x+4

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expand (x^3-6x^2+12x-8)/(x-2)

expand

\frac{x ^{3} - 6 x ^{2} + 12 x - 8}{x - 2}

x^{2} - 4 x + 4

Solution steps

\frac{x ^{3} - 6 x ^{2} + 12 x - 8}{x - 2}

Apply cube of difference rule:

a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} = (a - b)^{3}

a = x, b = 2

= \frac{( x - 2 ) ^{3}}{x - 2}

Cancel the common factor:

x - 2

= (x - 2)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = x, b = 2

= x^{2} - 2 x \cdot 2 + 2^{2}

Simplify

x^{2} - 2 x \cdot 2 + 2^{2} : x^{2} - 4 x + 4

= x^{2} - 4 x + 4

\frac{x + 1}{x ^{2} ( x ^{2} + 1 )}

(- 1)^{3}

(3 + 2 y + y^{2})^{5}

\frac{3 s ^{3} + 4 s ^{2} + 36 s + 16}{( s ^{2} + 4 ) ( s ^{2} - 4 )}

\frac{2 ( 2 s - 1 )}{2 s ^{2} - s - 2}

What is expand (x^3-6x^2+12x-8)/(x-2) ?
The solution to expand (x^3-6x^2+12x-8)/(x-2) is x^2-4x+4